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Glossary Physics (I-Introduction)
1 Glossary Physics (I-introduction) - Efficiency: The percent of the work put into a machine that is converted into useful work output; = work done / energy used [-]. = eta In machines: The work output of any machine cannot exceed the work input (<=100%); in an ideal machine, where no energy is transformed into heat: work(input) = work(output), =100%. Energy: The property of a system that enables it to do work. Conservation o. E.: Energy cannot be created or destroyed; it may be transformed from one form into another, but the total amount of energy never changes. Equilibrium: The state of an object when not acted upon by a net force or net torque; an object in equilibrium may be at rest or moving at uniform velocity - not accelerating. Mechanical E.: The state of an object or system of objects for which any impressed forces cancels to zero and no acceleration occurs. Dynamic E.: Object is moving without experiencing acceleration. Static E.: Object is at rest.F Force: The influence that can cause an object to be accelerated or retarded; is always in the direction of the net force, hence a vector quantity; the four elementary forces are: Electromagnetic F.: Is an attraction or repulsion G, gravit. const.6.672E-11[Nm2/kg2] between electric charges: d, distance [m] 2 2 2 2 F = 1/(40) (q1q2/d ) [(CC/m )(Nm /C )] = [N] m,M, mass [kg] Gravitational F.: Is a mutual attraction between all masses: q, charge [As] [C] 2 2 2 2 F = GmM/d [Nm /kg kg 1/m ] = [N] 0, dielectric constant Strong F.: (nuclear force) Acts within the nuclei of atoms: 8.854E-12 [C2/Nm2] [F/m] 2 2 2 2 2 F = 1/(40) (e /d ) [(CC/m )(Nm /C )] = [N] , 3.14 [-] Weak F.: Manifests itself in special reactions among elementary e, 1.60210 E-19 [As] [C] particles, such as the reaction that occur in radioactive decay. -
Convolution! (CDT-14) Luciano Da Fontoura Costa
Convolution! (CDT-14) Luciano da Fontoura Costa To cite this version: Luciano da Fontoura Costa. Convolution! (CDT-14). 2019. hal-02334910 HAL Id: hal-02334910 https://hal.archives-ouvertes.fr/hal-02334910 Preprint submitted on 27 Oct 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Convolution! (CDT-14) Luciano da Fontoura Costa [email protected] S~aoCarlos Institute of Physics { DFCM/USP October 22, 2019 Abstract The convolution between two functions, yielding a third function, is a particularly important concept in several areas including physics, engineering, statistics, and mathematics, to name but a few. Yet, it is not often so easy to be conceptually understood, as a consequence of its seemingly intricate definition. In this text, we develop a conceptual framework aimed at hopefully providing a more complete and integrated conceptual understanding of this important operation. In particular, we adopt an alternative graphical interpretation in the time domain, allowing the shift implied in the convolution to proceed over free variable instead of the additive inverse of this variable. In addition, we discuss two possible conceptual interpretations of the convolution of two functions as: (i) the `blending' of these functions, and (ii) as a quantification of `matching' between those functions. -
Introduction to Phasing Crystallography ISSN 0907-4449
research papers Acta Crystallographica Section D Biological Introduction to phasing Crystallography ISSN 0907-4449 Garry L. Taylor When collecting X-ray diffraction data from a crystal, we Received 30 August 2009 measure the intensities of the diffracted waves scattered from Accepted 22 February 2010 a series of planes that we can imagine slicing through the Centre for Biomolecular Sciences, University of St Andrews, St Andrews, Fife KY16 9ST, crystal in all directions. From these intensities we derive the Scotland amplitudes of the scattered waves, but in the experiment we lose the phase information; that is, how we offset these waves when we add them together to reconstruct an image of our Correspondence e-mail: [email protected] molecule. This is generally known as the ‘phase problem’. We can only derive the phases from some knowledge of the molecular structure. In small-molecule crystallography, some basic assumptions about atomicity give rise to relationships between the amplitudes from which phase information can be extracted. In protein crystallography, these ab initio methods can only be used in the rare cases in which there are data to at least 1.2 A˚ resolution. For the majority of cases in protein crystallography phases are derived either by using the atomic coordinates of a structurally similar protein (molecular replacement) or by finding the positions of heavy atoms that are intrinsic to the protein or that have been added (methods such as MIR, MIRAS, SIR, SIRAS, MAD, SAD or com- binations of these). The pioneering work of Perutz, Kendrew, Blow, Crick and others developed the methods of isomor- phous replacement: adding electron-dense atoms to the protein without disturbing the protein structure. -
Phase Retrieval Without Prior Knowledge Via Single-Shot Fraunhofer Diffraction Pattern of Complex Object
Phase retrieval without prior knowledge via single-shot Fraunhofer diffraction pattern of complex object An-Dong Xiong1 , Xiao-Peng Jin1 , Wen-Kai Yu1 and Qing Zhao1* Fraunhofer diffraction is a well-known phenomenon achieved with most wavelength even without lens. A single-shot intensity measurement of diffraction is generally considered inadequate to reconstruct the original light field, because the lost phase part is indispensable for reverse transformation. Phase retrieval is usually conducted in two means: priori knowledge or multiple different measurements. However, priori knowledge works for certain type of object while multiple measurements are difficult for short wavelength. Here, by introducing non-orthogonal measurement via high density sampling scheme, we demonstrate that one single-shot Fraunhofer diffraction pattern of complex object is sufficient for phase retrieval. Both simulation and experimental results have demonstrated the feasibility of our scheme. Reconstruction of complex object reveals depth information or refraction index; and single-shot measurement can be achieved under most scenario. Their combination will broaden the application field of coherent diffraction imaging. Fraunhofer diffraction, also known as far-field diffraction, problem12-14. These matrix complement methods require 4N- does not necessarily need any extra optical devices except a 4 (N stands for the dimension) generic measurements such as beam source. The diffraction field is the Fourier transform of Gaussian random measurements for complex field15. the original light field. However, for visible light or X-ray Ptychography is another reliable method to achieve image diffraction, the phase part is hardly directly measurable1. with good resolution if the sample can endure scanning16-19. Therefore, phase retrieval from intensity measurement To achieve higher spatial resolution around the size of atom, becomes necessary for reconstructing the original field. -
EMT UNIT 1 (Laws of Reflection and Refraction, Total Internal Reflection).Pdf
Electromagnetic Theory II (EMT II); Online Unit 1. REFLECTION AND TRANSMISSION AT OBLIQUE INCIDENCE (Laws of Reflection and Refraction and Total Internal Reflection) (Introduction to Electrodynamics Chap 9) Instructor: Shah Haidar Khan University of Peshawar. Suppose an incident wave makes an angle θI with the normal to the xy-plane at z=0 (in medium 1) as shown in Figure 1. Suppose the wave splits into parts partially reflecting back in medium 1 and partially transmitting into medium 2 making angles θR and θT, respectively, with the normal. Figure 1. To understand the phenomenon at the boundary at z=0, we should apply the appropriate boundary conditions as discussed in the earlier lectures. Let us first write the equations of the waves in terms of electric and magnetic fields depending upon the wave vector κ and the frequency ω. MEDIUM 1: Where EI and BI is the instantaneous magnitudes of the electric and magnetic vector, respectively, of the incident wave. Other symbols have their usual meanings. For the reflected wave, Similarly, MEDIUM 2: Where ET and BT are the electric and magnetic instantaneous vectors of the transmitted part in medium 2. BOUNDARY CONDITIONS (at z=0) As the free charge on the surface is zero, the perpendicular component of the displacement vector is continuous across the surface. (DIꓕ + DRꓕ ) (In Medium 1) = DTꓕ (In Medium 2) Where Ds represent the perpendicular components of the displacement vector in both the media. Converting D to E, we get, ε1 EIꓕ + ε1 ERꓕ = ε2 ETꓕ ε1 ꓕ +ε1 ꓕ= ε2 ꓕ Since the equation is valid for all x and y at z=0, and the coefficients of the exponentials are constants, only the exponentials will determine any change that is occurring. -
System Design and Verification of the Precession Electron Diffraction Technique
NORTHWESTERN UNIVERSITY System Design and Verification of the Precession Electron Diffraction Technique A DISSERTATION SUBMITTED TO THE GRADUATE SCHOOL IN PARTIAL FULFILLMENT OF THE REQUIREMENTS for the degree DOCTOR OF PHILOSOPHY Field of Materials Science and Engineering By Christopher Su-Yan Own EVANSTON, ILLINOIS First published on the WWW 01, August 2005 Build 05.12.07. PDF available for download at: http://www.numis.northwestern.edu/Research/Current/precession.shtml c Copyright by Christopher Su-Yan Own 2005 All Rights Reserved ii ABSTRACT System Design and Verification of the Precession Electron Diffraction Technique Christopher Su-Yan Own Bulk structural crystallography is generally a two-part process wherein a rough starting structure model is first derived, then later refined to give an accurate model of the structure. The critical step is the deter- mination of the initial model. As materials problems decrease in length scale, the electron microscope has proven to be a versatile and effective tool for studying many problems. However, study of complex bulk structures by electron diffraction has been hindered by the problem of dynamical diffraction. This phenomenon makes bulk electron diffraction very sensitive to specimen thickness, and expensive equip- ment such as aberration-corrected scanning transmission microscopes or elaborate methodology such as high resolution imaging combined with diffraction and simulation are often required to generate good starting structures. The precession electron diffraction technique (PED), which has the ability to significantly reduce dynamical effects in diffraction patterns, has shown promise as being a “philosopher’s stone” for bulk electron diffraction. However, a comprehensive understanding of its abilities and limitations is necessary before it can be put into widespread use as a standalone technique. -
Fresnel Diffraction.Nb Optics 505 - James C
Fresnel Diffraction.nb Optics 505 - James C. Wyant 1 13 Fresnel Diffraction In this section we will look at the Fresnel diffraction for both circular apertures and rectangular apertures. To help our physical understanding we will begin our discussion by describing Fresnel zones. 13.1 Fresnel Zones In the study of Fresnel diffraction it is convenient to divide the aperture into regions called Fresnel zones. Figure 1 shows a point source, S, illuminating an aperture a distance z1away. The observation point, P, is a distance to the right of the aperture. Let the line SP be normal to the plane containing the aperture. Then we can write S r1 Q ρ z1 r2 z2 P Fig. 1. Spherical wave illuminating aperture. !!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!! 2 2 2 2 SQP = r1 + r2 = z1 +r + z2 +r 1 2 1 1 = z1 + z2 + þþþþ r J þþþþþþþ + þþþþþþþN + 2 z1 z2 The aperture can be divided into regions bounded by concentric circles r = constant defined such that r1 + r2 differ by l 2 in going from one boundary to the next. These regions are called Fresnel zones or half-period zones. If z1and z2 are sufficiently large compared to the size of the aperture the higher order terms of the expan- sion can be neglected to yield the following result. l 1 2 1 1 n þþþþ = þþþþ rn J þþþþþþþ + þþþþþþþN 2 2 z1 z2 Fresnel Diffraction.nb Optics 505 - James C. Wyant 2 Solving for rn, the radius of the nth Fresnel zone, yields !!!!!!!!!!! !!!!!!!! !!!!!!!!!!! rn = n l Lorr1 = l L, r2 = 2 l L, , where (1) 1 L = þþþþþþþþþþþþþþþþþþþþ þþþþþ1 + þþþþþ1 z1 z2 Figure 2 shows a drawing of Fresnel zones where every other zone is made dark. -
Subwavelength Resolution Fourier Ptychography with Hemispherical Digital Condensers
Subwavelength resolution Fourier ptychography with hemispherical digital condensers AN PAN,1,2 YAN ZHANG,1,2 KAI WEN,1,3 MAOSEN LI,4 MEILING ZHOU,1,2 JUNWEI MIN,1 MING LEI,1 AND BAOLI YAO1,* 1State Key Laboratory of Transient Optics and Photonics, Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi’an 710119, China 2University of Chinese Academy of Sciences, Beijing 100049, China 3College of Physics and Information Technology, Shaanxi Normal University, Xi’an 710071, China 4Xidian University, Xi’an 710071, China *[email protected] Abstract: Fourier ptychography (FP) is a promising computational imaging technique that overcomes the physical space-bandwidth product (SBP) limit of a conventional microscope by applying angular diversity illuminations. However, to date, the effective imaging numerical aperture (NA) achievable with a commercial LED board is still limited to the range of 0.3−0.7 with a 4×/0.1NA objective due to the constraint of planar geometry with weak illumination brightness and attenuated signal-to-noise ratio (SNR). Thus the highest achievable half-pitch resolution is usually constrained between 500−1000 nm, which cannot fulfill some needs of high-resolution biomedical imaging applications. Although it is possible to improve the resolution by using a higher magnification objective with larger NA instead of enlarging the illumination NA, the SBP is suppressed to some extent, making the FP technique less appealing, since the reduction of field-of-view (FOV) is much larger than the improvement of resolution in this FP platform. Herein, in this paper, we initially present a subwavelength resolution Fourier ptychography (SRFP) platform with a hemispherical digital condenser to provide high-angle programmable plane-wave illuminations of 0.95NA, attaining a 4×/0.1NA objective with the final effective imaging performance of 1.05NA at a half-pitch resolution of 244 nm with a wavelength of 465 nm across a wide FOV of 14.60 mm2, corresponding to an SBP of 245 megapixels. -
Optical Ptychographic Phase Tomography
University College London Final year project Optical Ptychographic Phase Tomography Supervisors: Author: Prof. Ian Robinson Qiaoen Luo Dr. Fucai Zhang March 20, 2013 Abstract The possibility of combining ptychographic iterative phase retrieval and computerised tomography using optical waves was investigated in this report. The theoretical background and historic developments of ptychographic phase retrieval was reviewed in the first part of the report. A simple review of the principles behind computerised tomography was given with 2D and 3D simulations in the following chapters. The sample used in the experiment is a glass tube with its outer wall glued with glass microspheres. The tube has a diameter of approx- imately 1 mm and the microspheres have a diameter of 30 µm. The experiment demonstrated the successful recovery of features of the sam- ple with limited resolution. The results could be improved in future attempts. In addition, phase unwrapping techniques were compared and evaluated in the report. This technique could retrieve the three dimensional refractive index distribution of an optical component (ideally a cylindrical object) such as an opitcal fibre. As it is relatively an inexpensive and readily available set-up compared to X-ray phase tomography, the technique can have a promising future for application at large scale. Contents List of Figures i 1 Introduction 1 2 Theory 3 2.1 Phase Retrieval . .3 2.1.1 Phase Problem . .3 2.1.2 The Importance of Phase . .5 2.1.3 Phase Retrieval Iterative Algorithms . .7 2.2 Ptychography . .9 2.2.1 Ptychography Principle . .9 2.2.2 Ptychographic Iterative Engine . -
Wide-Field, High-Resolution Fourier Ptychographic Microscopy
Wide-field, high-resolution Fourier ptychographic microscopy Guoan Zheng*, Roarke Horstmeyer, and Changhuei Yang Electrical Engineering, California Institute of Technology, Pasadena, CA 91125, USA *Correspondence should be addressed to: [email protected] Keywords: Ptychography; high-throughput imaging; digital wavefront correction; digital pathology Manuscript information: 11 text pages, 4 figures Supporting materials: 2 text pages, 8 figures, 1 video Abstract: In this article, we report an imaging method, termed Fourier ptychographic microscopy (FPM), which iteratively stitches together a number of variably illuminated, low-resolution intensity images in Fourier space to produce a wide-field, high-resolution complex sample image. By adopting a wavefront correction strategy, the FPM method can also correct for aberrations and digitally extend a microscope's depth-of-focus beyond the physical limitations of its optics. As a demonstration, we built a microscope prototype with a resolution of 0.78 μm, a field-of-view of approximately 120 mm2, and a resolution-invariant depth-of-focus of 0.3 mm (characterized at 632 nm). Gigapixel color images of histology slides verify FPM's successful operation. The reported imaging procedure transforms the general challenge of high-throughput, high- resolution microscopy from one that is coupled to the physical limitations of the system's optics to one that is solvable through computation. The throughput of an imaging platform is fundamentally limited by its optical system’s space- bandwidth product (SBP)1, defined as the number of degrees of freedom it can extract from an optical signal. The SBP of a conventional microscope platform is typically in megapixels, regardless of its employed magnification factor or numerical aperture (NA). -
Introduction to Light Microscopy
Introduction to light microscopy A CAMDU training course Claire Mitchell, Imaging specialist, L1.01, 08-10-2018 Contents 1.Introduction to light microscopy 2.Different types of microscope 3.Fluorescence techniques 4.Acquiring quantitative microscopy data 1. Introduction to light microscopy 1.1 Light and its properties 1.2 A simple microscope 1.3 The resolution limit 1.1 Light and its properties 1.1.1 What is light? An electromagnetic wave A massless particle AND γ commons.wikimedia.org/wiki/File:EM-Wave.gif www.particlezoo.net 1.1.2 Properties of waves Light waves are transverse waves – they oscillate orthogonally to the direction of propagation Important properties of light: wavelength, frequency, speed, amplitude, phase, polarisation upload.wikimedia.org 1.1.3 The electromagnetic spectrum 퐸푝ℎ표푡표푛 = ℎν 푐 = λν 퐸푝ℎ표푡표푛 = photon energy ℎ = Planck’s constant ν = frequency 푐 = speed of light λ = wavelength pion.cz/en/article/electromagnetic-spectrum 1.1.4 Refraction Light bends when it encounters a change in refractive index e.g. air to glass www.thetastesf.com files.askiitians.com hyperphysics.phy-astr.gsu.edu/hbase/Sound/imgsou/refr.gif 1.1.5 Diffraction Light waves spread out when they encounter an aperture. electron6.phys.utk.edu/light/1/Diffraction.htm The smaller the aperture, the larger the spread of light. 1.1.6 Interference When waves overlap, they add together in a process called interference. peak + peak = 2 x peak constructive trough + trough = 2 x trough peak + trough = 0 destructive www.acs.psu.edu/drussell/demos/superposition/superposition.html 1.2 A simple microscope 1.2.1 Using lenses for refraction 1 1 1 푣 = + 푚 = physicsclassroom.com 푓 푢 푣 푢 cdn.education.com/files/ Light bends as it encounters each air/glass interface of a lens. -
Fraunhofer Diffraction Effects on Total Power for a Planckian Source
Volume 106, Number 5, September–October 2001 Journal of Research of the National Institute of Standards and Technology [J. Res. Natl. Inst. Stand. Technol. 106, 775–779 (2001)] Fraunhofer Diffraction Effects on Total Power for a Planckian Source Volume 106 Number 5 September–October 2001 Eric L. Shirley An algorithm for computing diffraction ef- Key words: diffraction; Fraunhofer; fects on total power in the case of Fraun- Planckian; power; radiometry. National Institute of Standards and hofer diffraction by a circular lens or aper- Technology, ture is derived. The result for Fraunhofer diffraction of monochromatic radiation is Gaithersburg, MD 20899-8441 Accepted: August 28, 2001 well known, and this work reports the re- sult for radiation from a Planckian source. [email protected] The result obtained is valid at all temper- atures. Available online: http://www.nist.gov/jres 1. Introduction Fraunhofer diffraction by a circular lens or aperture is tion, because the detector pupil is overfilled. However, a ubiquitous phenomenon in optics in general and ra- diffraction leads to losses in the total power reaching the diometry in particular. Figure 1 illustrates two practical detector. situations in which Fraunhofer diffraction occurs. In the All of the above diffraction losses have been a subject first example, diffraction limits the ability of a lens or of considerable interest, and they have been considered other focusing optic to focus light. According to geo- by Blevin [2], Boivin [3], Steel, De, and Bell [4], and metrical optics, it is possible to focus rays incident on a Shirley [5]. The formula for the relative diffraction loss lens to converge at a focal point.